IntegratedGaussianPRF¶
- class photutils.psf.IntegratedGaussianPRF(sigma=1, x_0=0, y_0=0, flux=1, **kwargs)[source]¶
Bases:
Fittable2DModel
Circular Gaussian model integrated over pixels.
Because it is integrated, this model is considered a PRF, not a PSF (see Terminology for more about the terminology used here.)
This model is a Gaussian integrated over an area of
1
(in units of the model input coordinates, e.g., 1 pixel). This is in contrast to the apparently similarastropy.modeling.functional_models.Gaussian2D
, which is the value of a 2D Gaussian at the input coordinates, with no integration. So this model is equivalent to assuming the PSF is Gaussian at a sub-pixel level.- Parameters:
- sigmafloat
Width of the Gaussian PSF.
- fluxfloat, optional
Total integrated flux over the entire PSF
- x_0float, optional
Position of the peak in x direction.
- y_0float, optional
Position of the peak in y direction.
Notes
This model is evaluated according to the following formula:
\[f(x, y) = \frac{F}{4} \left[ {\rm erf} \left(\frac{x - x_0 + 0.5} {\sqrt{2} \sigma} \right) - {\rm erf} \left(\frac{x - x_0 - 0.5} {\sqrt{2} \sigma} \right) \right] \left[ {\rm erf} \left(\frac{y - y_0 + 0.5} {\sqrt{2} \sigma} \right) - {\rm erf} \left(\frac{y - y_0 - 0.5} {\sqrt{2} \sigma} \right) \right]\]where
erf
denotes the error function andF
the total integrated flux.Attributes Summary
Names of the parameters that describe models of this type.
Methods Summary
evaluate
(x, y, flux, x_0, y_0, sigma)Model function Gaussian PSF model.
Attributes Documentation
- flux = Parameter('flux', value=1.0)¶
- param_names = ('flux', 'x_0', 'y_0', 'sigma')¶
Names of the parameters that describe models of this type.
The parameters in this tuple are in the same order they should be passed in when initializing a model of a specific type. Some types of models, such as polynomial models, have a different number of parameters depending on some other property of the model, such as the degree.
When defining a custom model class the value of this attribute is automatically set by the
Parameter
attributes defined in the class body.
- sigma = Parameter('sigma', value=1.0, fixed=True)¶
- x_0 = Parameter('x_0', value=0.0)¶
- y_0 = Parameter('y_0', value=0.0)¶
Methods Documentation